In this paper, extended projective Riccati equation method is presented for constructing more new exact solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than pro...In this paper, extended projective Riccati equation method is presented for constructing more new exact solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the effect of the method, Broer Kaup Kupershmidt system is employed and Jacobi doubly periodic solutions are obtained. This algorithm can also be applied to other nonlinear differential equations.展开更多
In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule o...In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule of the rogue wave solutions up to fourth-order. These solutions have two parameters a and ;3 which denote the contribution of the higher-order terms （dispersions and nonlinear effects） included in the HONLS equation. Two localized properties, i.e., length and width of the first-order rogue wave solution are expressed by above two parameters, which show analytically a remarkable influence of higher-order terms on the rogue wave. Moreover, profiles of the higher-order rogue wave solutions demonstrate graphically a strong compression effect along t-direction given by higher-order terms.展开更多
基金the State Key Basic Research Development Program of China under Grant No.2004CB318000
文摘In this paper, extended projective Riccati equation method is presented for constructing more new exact solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the effect of the method, Broer Kaup Kupershmidt system is employed and Jacobi doubly periodic solutions are obtained. This algorithm can also be applied to other nonlinear differential equations.
基金Supported by the National Natural Science Foundation of China under Grant No.11271210the K.C.Wong Magna Fund in Ningbo University
文摘In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule of the rogue wave solutions up to fourth-order. These solutions have two parameters a and ;3 which denote the contribution of the higher-order terms （dispersions and nonlinear effects） included in the HONLS equation. Two localized properties, i.e., length and width of the first-order rogue wave solution are expressed by above two parameters, which show analytically a remarkable influence of higher-order terms on the rogue wave. Moreover, profiles of the higher-order rogue wave solutions demonstrate graphically a strong compression effect along t-direction given by higher-order terms.
